Sometimes people say that water is removed from clothes in iy87cah-w dg .r nwu 9-jc/5wva spin dryer by centrifugal forcca /w7hnjyc v-. 8wuwr5-g di9e throwing the water outward. What is wrong with this statement?

Will the acceleration of u.p w yj cn3paddz)2xi;bq o86zh(/9a a car be the same when the car travels around a sharp curve at 3iub)dp;d.naq92/aj(z y 6o8xc pzh w a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car exeu6 -erikqkcr;,t :wwztjx*+)rt the greatest and least forces ouw;q cr,-t jz +r:it6wkx) ke*n the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridin1qpx,z+ e3k0k pak *oag a horse on a merry-go-round. Which *01kazoep q+ak,3kp xof these forces provides the centripetal acceleration of the child?

A bucket of water can bcy36x si.u6 sqy;qj0ht5x /q wrhhz30e whirled in a vertical circle without the water spilling out, even at the top of the circle whe yt3sq c;h0qyr.q3xhix/6uz05h sj6 wn the bucket is upside down. Explain.

How many “accelerators” do you have in your ,ibzw2fzmqbymt,/)4 car? There are at least three controls in the car which can be used to cause th,2fizyz,mq b t)mb/4 we car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as sho6j 5/wmquf/vhwn in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels th vmh/qw5u j6/fe normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speeusue 6+vsj,y4d?

Why do airplanes bank when they turn? How wouldojej y6 .)edb;ar+0ow you compute the banking angle givend r; a0owbej)oej+y.6 its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a x7by)- wshkqyu)w-, v horizontal plane. She wants to let go at precisely the right time so that the ba7x--yyq,vukb h))w wsll will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force ogtqf5i io;4le7fv w,po2o.) e n the Earth? If so, how large a force? fp ;,qwieg)45fi7e . to olo2vConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, 5ilr;0w q sgqm-ff5hgwie97 ( in what ways would the Moon’s orbit be diffwg7qrsf (fqig ;mwil9h0- 5e5erent?

Which pulls harder gravitationally, the Earth .c1x ;2krfd1 a0,*dbtdc xwzson the Moon, or the Moon on the Earth? Which accele,xxw.0 c*frdazk1d1b ds;t2c rates more?

The Sun's gravitational pull o)cx2myk*1i(p39zoe73wzl du t w6 o hqn the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from onelo mi(z 9h72d ecq3yw6 *uxt)1zk3wop side of the Earth to the other.]

Will an object weigh mktiun h2r7har6*3c)z ore at the equator or at the poles? What two effects are at work? Do tiru3 c6 azn2hrkh*t) 7hey oppose each other?

The gravitational force on the Moon due to the Earth is only abou wbihzj*, p(u5t half the force on the Moon due to the Sun. Why isnjz5uhib w* p(,’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sunlpo0 :n-2opuy acf+5k larger or smaller than the centripetal accelkcu+ 2 lpo-0:f5anpo yeration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or-gdj3al4g k1u (b) toward the west? Consider the Earth’s rotation dl1k-gag ju3 4direction.

When will your apparent weight be the gl* 4m9t( 0zdjbov qb1alsm c4.reatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward4( 9sm qz.cbvolja1*d04btm l , (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outf6o h4jnn8ti .er space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell t4hn.io8n6jft hat rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent vaze 8d fskf2ti1j9mc; -8/lsh 6 uk:vweightlessness” between sv/iz:lk6-f8cjm2 u sth k s8fevda19;teps.

The Earth moves faster in its orbit around the Sun in January than in July. Isa02 ,ltbe):k - j7np zs1vpyqy the Earth closer to the Sun in January, or in July? Explain0z:by7)la ,vyk 12tn p qsjp-e. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to 5epg)ggs2ap.2 jfm 4a have a moon. Explain how this2s e j4g2aa5gf gp)p.m discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much la)x rw4g(tri s8rger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a spr stg() ir84wxeed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 198iv(ezw6 g)ey +n,kx1 e0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the o3 e cae(yf9+hye -)xmgnbo(/Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of rae3yoe b-nofe (ch) (+9mg/x yadius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discu8h03cryxq7;k9iis fas as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the di7yf xarq ii8c0kh39;s scus.   

  Suppose the space shuttle is in orbit 400 km frolxp4gl fv9bso8:zl d1,a gh n;*f8tg9m the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of l 4x g9vhf8gn*;tlg8bdal9o1,:f zs p the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of c8* zcb0iberu7 lay on the edge of a potter’s wheel tub*u zc7e b0r8irning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertsc b:u5bdd49di. ndm0 ical circle of radius 72.0 cm , as shown in .: 90du4d dicmnb5sbd Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn - y.epcr.mgw2of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indee.y.g -mcwpr2pendent of the mass of the car?   

  How large must the coefficient of static friction be between the tirtjxw ; jh*//eces and the road if jec/xhj* t/w;a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet f z,h1m0 zcg6ayighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how cag0h1ymz z6 ,fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm froljw 5v3,8rri xy9my*j70qvr r2 dfca(m the axis of a rotating turntable of variable speed. When the speed of the turnta9 vaqv( jm0,ji8r d53lx7cwr*2fry y rble is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travelwak7i*p 8unfsg 33tjh dl4n9c;u;u(d ing when upside down at the top of a kl;;swd4j9 h(i u*n3af8tudc 3 7gpnucircle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the drive(/)j ve(cpgn yr) crosses the rounded top of a hill (radiy cp gj(()/envus =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameterr 8mdcu*lm7;w 5div;s lfr45m Ferris wheel need to make for the pa8 dlcmumw;r;rm 5d l s5f47*vissengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle o* o e esh5d6qyqb98)gdf radius 1.10 m. At the lowest point of qyh9 qb d8d)sege6* o5its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm fr9dbow x 8wxso0e5 lx(0om the axis of rotation is to experience an accelew5bxwo9e do 80 x0x(lsration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotat-p g4lw b)..vn p(e4* g d,gwk5wxifszed in a cylindrically walled "rwpl)fv5ek4 n. gi* zb-ggpd4(wwsx.,oom." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a cir6rr1 wkf6k( j.jui,efsc- w7bcle on a frictionless air-hockey tabletop, and is held j (w6e sb.krf7c6 ju- 1,irkwfin this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight ofemnv48 es,j.g the ball which revolves on jme n .vs,g4e8a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m 3c6zk91r:z arir3oy q dyp;n 9is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses /gu3zvsdz1( )7cft9 hm tcg ;v$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver od, v ma:u2ypzc)1x( vby diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripe4.xtbf qox20b l;(uqv fg8:nztal components of the net force exerted on the car (bfbl8 xnvq(tqu2: f o4;g.b zx0y the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, goingu8/xr+q t6y in(-zlh q from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the roal/6izq tr-+nyhu8 q(x d to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular i ys-)+ fyij0z fe:izkzu cf1++nszff0 iy1) yke+fc :uz j+zi+-stant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km og )12xn7 nnip(2 Earth radii) above71 ox2) nnngpi the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mawd** yy4c*y )my0zivl.d2oysq z61rxwso 8 -q gnitzow)zds-yyyqy0do .i 86*wx*qr2sy 1lc4vm * ude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the accelerajubx79ko 1p ,x9x9itvtion due to gravity on the Moon. The Moon's radius is 1.79 txjbo 199pxki7vu, x4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical plane pojb183c n2vdpo4b f-t has a radius 1.5 times that of Earth, but has the same mass. What is th 31nbd2ocv84o-j f ppbe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but thy-pcrsrb r11p17 jb.b e same radius. What is g near its surface cbb1rs p17 .yjprbr1-?   

  Two objects attract each other gravitationally with a force of 2.5c0l-w hn/ um/q$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value ofj a(gwzhg2 6/ pe+bb4nws8ni3 g , the acceleration of gravity, at (a) 3200 mz63284ha/geib(bw w gjspnn+    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outs)zu23es fgysrwg -y(s*e7xni z *.lp4ide the Earth where thegravi(se7 2zfnyg- 4eyiw.p*lu3* grssz x)tational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star ha to0ng:.1gkp; n3yxi ws five times the mass of our Sun packed into a sphere a yn0 xp3.g;tkw1:ingobout 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star liby1)); t 3ga7cqf octf;1h mj)io+wodke our Sun but is now in the last stage of its fqioa7jf+byh c3)t;tod)w m 1)cg;1o evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the snftjf uime ,06 jj)6p)pace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms fjfj)p6je,n 0t) ui m6of g.   

  Four 9.5-kg spheres are locat;7mp) kker:3vhn iep) ed at the corners of a square of side 0.60 m. Calculate );7me:rv3kkehpi)p n the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side od 5rm7 k3g,vjmf the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming35mkgrj , dmv7 all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.oo. (2w3qb w pf2ysh(z38 of what itz2f(3w w qsp2o.ybh (o is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using-27dytl 1wcbv the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Keplev-c7l 1dbw yt2r’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cn wz if+;9cc.vc)gp- circular orbit about the Earth at a height of 36 nv wp-zccc).gfc+;i900 km.    $\times 10^3$

  The space shuttle releases a sa ibe tj86*sc0kyv5,i+nwhm6 btellite into a circular orbit 650 km above the Earth. How fast must the s8c,h b*iy ksw 5n66bej v+m0ithuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occuhj;4bz un4857jqtbxq9 y*(ds yqc 6vypants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time cj8b(74yy;qt4 qu*b x56dzvyq ns hj9needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eara 2vgw l 1axx;zwl+hz /g7pn14th in a circular “near-Earth” orbit. A “near-Earth” orbila4zp1n;1 /xzwx+2wglh 7a vgt is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched frop u+pzx/vu jq5. td-p+m the top of 5zx ud +p+.qp/ -utjvpMt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landingn 7nhrw5 07bap)a9t da mission, the command module continued to orbit the Moon at an altitude of ab7 nwrh9dna)a5 a7 t0pbout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn zqyy.drv 8z.4a ,k/8a :is jniare composed of chunks of ice that orbit the planet. The inner radius of the rinzjz: .qr4ni8a vy8yi/ s,kd. ags is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter ro;/)*rzdk0o fkx rmgjt-0w1p jtates once every 15.5 s (see Fig. 5–9). What jgpomxrwr )- *1tkz0k;jf0/ d is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight oizij2c;t8n+ 4k,sr zz f a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicl4z8j ;siintcr2z, k +ze (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star syste,rfec 7ma s3/sm consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point 3ra7es /sfmc, midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in p z ;;96ste-gm l)feys71wir aan elevator that moves ea l;;rg9 pm6 sif)steyw1-7z
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hang,q4.sf/0m v 9olmuc x*cjl3hjs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. Wjho q0m sx 93lv*j4m,./clfuc hat was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the hpl-h 4zjj(:y r .6fm1emfu4qsurface of a planet with period T , the density (mass/volume) of the pymj:-q4.rzeh1mup64j h lf(f lanet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 abni)j .g6i ,1g7bqpc ;:poypd) to determine the period of an artificial satellite gq;bnpiog jip .:76y b ca)p1,orbiting very near the Earth’s surface.    s

  The asteroid Icarus, o8.hty:jrnl/4 xv0j jthough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its m8hyojjtl0:.4xn v/ r jean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dism1d6d w) yhzyiz+ca,*+ lpkv0tance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roug3;1pmgpnbe v4m)w l. qhly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar Swpv m4.ngm) 1 pe;bl3qystem? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about then l a:gzr+u/eqy.1t:d.: yjxe center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean disyi ( b 4p.p4r5h9oqtyxtance for the four largest moons of Jupiter (those discovered by t9( opxy q p5i4h.4yrbGalileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period c6x)rd g 13bh c, ko-,a1f1ss lg4tzgsand distance of the Moon. 4)b1gdc o1 sss3g ac-xz1k6,t rfg ,hl   $\times 10^{24}$

  Determine the mean dista)q bo p5i,b0lance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the p0 lqipbb,ao)5 eriods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betw1z qn-mdkpuc8;z9 1 ,(tuxbuxeen Mars and Jupiter consists of many fragments (which some space xp(1dzz 19-n;qx t8,uubckumscientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planetnu+o3;vki6+p r e :kuu" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always nooep+:n63+u;v ku kir oun). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig.8 h p w9-irgnor1;wjtzpng /(5 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of h1/;n torj9wnihpgw g(rp5-8z is swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be d;n mg:7 btmp1half what it is on the s1t: n mg7;pbmdurface?    $\times 10^6$

  On an ice rink, two skate;yauxf s(z ;;prs of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling z(au;; xyfp;s on one another?    $\times 10^2$

  Because the Earth rotate*w)ggjq.kp )vs once per day, the apparent acceleration of gravity at the equator is slightly) gw *qpv.kg)j less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will zj2ez nu6t),ta spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal anju 2zt,z) 6tend opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a batq, h0) j (pcfdcgs1ta+ho0 5 z:4n+hjxxvif-dhroom scale in an elevator, it says your mass is 82 kg. What is x( pv fx5a04dgh qzo,n 1-dhf0t+ c:)jjihc+sthe acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube tha8vs3-,y v0s(wgyebg hyaw 5l:)p g7ju6kt) uzt will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 htywysl,3a w85yj7:) 6buegk0 vggv) z-ups (km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop djt kqa;in f+evsvt +.vl+:6:(Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the acceledb t -hh4qc3kl1s,a9nration due to gravity at its surfah9n ,b3hkt1c l-d 4aqsce and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertic j1ihxz0 try :;yl:,thal by an ay lrth01,zj xt;::iyhngle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a desde cyk2)l4:kr ign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle kl: 2r e4)cdkythe curve?

  How long would a day be if the Earth were rotatinga3coh by;y y283b-l ds so fast that objects at the equator were apparently wei slbda8 -3;c23ybyyhoghtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dib) ym; bvrf)m11cn 5ghstance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 +x f0e,mzbk2p m. A lamp suspen+zkm2xf,0b p eded from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has beeno+ si656 anfy5i-5zms1 svnmo claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the s1 voo56n55isi+n6 s-ymm fza following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble n 6c f,j)6obn5d* wj0(g o5dfkro8hebSpace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be bgef6rn* kf58o(o ddc n )5bhw0j, j6o780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it vt5 8;.vp u4x46 o8vwb mgobqqtraverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Exgq68omqb;v b44x8 to 5p.uw vvplain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a ivfj(6 tk716kbqbp/ ugroup of 24 satellites orbiting the Earth. Usin (vi 6kfku tb1q/7bp6jg “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is mem 1tkllm:,no/4 h vcy8ant to orbit the asterotc:yhn1,ml 4km v /ol8id Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of rep , mq7,czedc ye)bh,/dztxwl gg7k9 9)air. You are in a circular orbit of the same radius as the se qd gc zt, 7/kdyec,)z,x9lb w7h)g9matellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000b v. e 1q5gmqg:yq2wq08s2vuj years. (a) What is its mean distance from t y 5mbe0v18g.vws2qq2quq j:g he Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you cwsw 9r*vgd ur6 /4m+evould actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, wvswgd eur+9m6/* 4rvlike F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Waisy7 -e s,wf8ey Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cw8i7fsys ,e -eenter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on ea/c0je, v:;guhz*k a bjch side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side b*;:h/ gc uevjz,ja0k of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 k;j,2xpj,s55op g2x8unjlzc 0x ryl :lg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the t7( es(relm-e,.yc hotip of the 1.5-cm-long sweep second hand on your w. soe(yel t 7m-c,ehr(rist watch?    $\times 10^{-4}$

  While fishing, you get bored and . z:45s5loxhrco av/hstart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing linlazco5vxh4 5 h.so/ r:e. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in ab+( 8eaiz0swprn hze9-, ysl9 new highway is designed so that a car travel( 9h+0 s-98,sewabepliy n zrzing at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, ut997r*lj5y *c irzh xupilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the mcru*h75zp 9lyr j*9ixain force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$